Solution manual for engineering fluid mechanics 11th edition by elger

1.12: PROBLEM DEFINITIONSituation: What is the approximate mass in units of slugs for a.. 1.17: PROBLEM DEFINITIONFind:How are density and speci…c weight related?. PLANConsider their de…

1.1: PROBLEM DEFINITIONApply critical thinking to an engineering-relevant issue that is important to you.Create a written document that lists the issue, your reasoning, and your conclusion.SOLUTION

Student answers will vary

NOTE TO INSTRUCTOR:

See Appendix A of this Chapter 1 Solution Manual document for active learningin-class activities that may be used as a follow-on to this assignment

Do research on the internet, then create a written document in which you(a) de…ne what inductive reasoning means and give two concrete examples, and(b) de…ne what deductive reasoning means and give two concrete examples.

Use the CT process to justify your reasoning and your conclusions

SOLUTIONStudent answers will vary

crite-1.3: PROBLEM DEFINITIONPick an engineered system that really motivates you From your favorite engineeredsystem, draft your own de…nition of engineering Then, see if your de…nition ofengineering …ts the de…nition of engineering in §1.1 How does this de…nition comparewith yours? What is similar? What is di¤erent?

SOLUTIONStudent answers will vary

NOTE TO INSTRUCTOR:

See Appendix A of this Chapter 1 Solution Manual document for active learningin-class activities that may be used as a follow-on to this assignment

Select an engineered design (e.g., hydroelectric power as in a dam, an arti…cial heart)that involves ‡uid mechanics and is also highly motivating to you Write a one-pageessay that addresses the following questions: Why is this application motivating toyou? How does the system you selected work? What role did engineers play in thedesign and development of this system?

SOLUTIONStudent answers will vary

NOTE TO INSTRUCTOR:

See Appendix A of this Chapter 1 Solution Manual document for active learningin-class activities that may be used as a follow-on to this assignment

1.5: PROBLEM DEFINITIONSituation:

(T/F) A ‡uid is de…ned as a material that continuously deforms under the action of

a normal stress

Issue:

Is the following statement best characterized as true or as false?

A ‡uid is de…ned as a material that continuously deforms under the action of a normalstress

REASONING:

1 By de…nition, a ‡uid is a material that deforms continuously under the action of

a “shear stress.”

2 The statement states “normal stress.”

3 Thus, the given statement is false

4 Another reason why the given statement is false is that it is easy to …nd examples inwhich the given statement is not true For example, ‡uid particles in a lake experiencenormal stresses and there is no ‡ow (i.e deformation)

CONCLUSION: The best answer is false

ap-No solution provided; answers will vary Possible answers could be determined bygoogling "material properties", which would yield answers such as thermal conduc-tivity, electrical conductivity, tensile strength, etc The next step would be to discusshow each new material property was di¤erent for solids, liquids, and gases.

1.7: PROBLEM DEFINITIONSituation:

Based on molecular mechanisms, explain why aluminum melts at 660 C whereas icemelts at 0 C

SOLUTIONWhen a solid melts, su¢ cient energy must be added to overcome the strong intermole-cular forces The intermolecular forces within solid aluminum require more energy

to be overcome (to cause melting), than do the intermolecular forces in ice

A ‡uid particle

a is de…ned as one molecule

b is a small chunk of ‡uid

c is so small that the continuum assumption does not applySOLUTION

The correct answer is b

1.9: PROBLEM DEFINITIONSituation:

The continuum assumption (select all that apply)

a applies in a vacuum such as in outer space

b assumes that ‡uids are in…nitely divisible into smaller and smaller parts

c is an invalid assumption when the length scale of the problem or design is similar

to the spacing of the molecules

d means that density can idealized as a continuous function of position

e only applies to gasesSOLUTION

The correct answers are b, c, and d

Note: Student answers will vary The CT process format (Issue/Reasoning/Conclusion)should be used.

An example answer is provided here

Issue:

A lift force on an airfoil is caused by air pressure on the bottom of the wing relative

to the top of the wing Therefore, lift force is a pressure force Use the CT process(see §1.1) to answer whether lift acting on an airfoil is a surface force, or a body force.Reasoning:

Pressure forces and lift forces have molecules of ‡uid touching the surface of thewing, and touching is the distinguishing feature of a surface force Therefore, lift

is a surface force, not a body force A body force is one caused by a …eld, such as

a magnetic, gravitational, or electrical …eld Although gravity in‡uences the pressuredistribution in the atmosphere where the plane is ‡ying, the lift (surface) force actsonly because the air is pressed against (touching) the airfoil surface

Conclusion:

A lift force is a surface force

1.11: PROBLEM DEFINITIONSituation:

Fill in the blanks Show your work, using conversion factors found in Table F.1(EFM11e)

PLAN

Do these unit conversions between di¤erent mass units

Show your work - e.g canceling and carrying units, using conversion factors found inTable F.1 (EFM11e)

a)SOLUTION 900 g is _ slug

20 g = 0:0617 slugb)

SOLUTION 27 lbm is kg

27 lbm = 27lbm

1

1 kg2:205 lbm

27 lbm = 12.2 kgc)

SOLUTION 100 kg is slugs

100 kg = 100 kg

1

1 slug14:59 kg

100 kg = 6.85 slugd)

1.12: PROBLEM DEFINITION

Situation:

What is the approximate mass in units of slugs for

a A 2-liter bottle of water?

b A typical adult male?

c A typical automobile?

a)PLANMass in slugs for: 2-L bottle of waterSOLUTION

PLANAnswers will vary, but for 180-lb male:

PLANAnswers will vary, but for 3000-lb automobile:

Answer the following questions related to mass and weight Show your work, andcancel and carry units.

PLANUse F = ma, and consider weight and mass units

In particular, be aware of consistent units and their de…nitions, such as:

1:0 N 1:0 kg 1:0 m= s2 and 1:0 lbf 1:0 slug 1:0 ft= s2a)

SOLUTION What is the weight (in N) of a 100-kg body?

F = m a on earth

W = (100 kg) 9:81 m= s2

W = 981 Nb)

SOLUTION What is the mass (in lbm) of 20 lbf of water?

SOLUTION What is the mass (in slugs) of 20 lbf of water?

m = F=a

m = 0:621 slug;

d)SOLUTION How many N are needed to accelerate 2 kg at 1 m/s2?

F = (2 kg) 1 m= s2

F = 2 Ne)

SOLUTION How many lbf are needed to accelerate 2 lbm at 1 ft/ s2?

m = 2 lbm convert to slugs for consistent units

2 lbm = 2 lbm

1

1 slug32:17 lbm

2lbm = 0:06217 slug Now, use F = m a with the consistent units

F = 0:06217 slug 1 m= s2

F = 0:0622 lbff)

SOLUTION How many lbf are needed to accelerate 2 slugs at 1 ft/ s2?

Here, units are already consistent

F = 2 slug 1 m= s2

F = 2 lbf

Situation: The sketch shows ‡uid ‡owing over a ‡at surface.

Find: Show how to …nd the value of the distance y where the derivative dV =dy ismaximum

REASONING

CONCLUSION(S)

The derivative is maximum where y = 0 cm

1.15: PROBLEM DEFINITIONSituation: An engineer measured the speed of a ‡owing ‡uid as a function of thedistance y from a wall; the data are shown in the table.

Find: Show how to calculate the maximum value of dV/dy for this data set Expressyour answer in SI units

REASONINGApply the de…nition of the derivative

CONCLUSION(S)

The maximum value of dV/dy is 1000 s 1

Situation: The plot shows data taken to measure the rate of water ‡owing into a tank

1.17: PROBLEM DEFINITIONFind:

How are density and speci…c weight related?

PLANConsider their de…nitions (conceptual and mathematical)SOLUTION

Density is a [mass]/[unit volume], and speci…c weight is a [weight]/[unit volume].Therefore, they are related by the equation = g , and density di¤ers from speci…cweight by the factor g, the acceleration of gravity

1.19: PROBLEM DEFINITIONSituation:

Which of these are units of density? (Select all that apply.)

a kg/m3

b mg/cm3

c lbm/ft3

d slug/ft3SOLUTIONCorrect answers are a, b, c, and d Each of these is a mass/volume

If a gas has = 14 N/m3 what is its density?

State your answers in SI units and in traditional units

SOLUTIONDensity and speci…c seight are related according to

=g

gFor = 14 N

= 2.78 10 3 slugft3

1.21: PROBLEM DEFINITIONSituation:

Calculate the number of molecules in:

a) One cubic cm of water at room conditionsb) One cubic cm of air at room conditionsa)

2 To determine the number of moles:

number of moles = (0:0010 kg) 1 mol

18 g

1000 g

1 kgnumber of moles = 0:055 mol

3 Using Avogadro’s number

(0:055 mol) 6 10

23moleculesmol

number of molecules = 3.3 1022 moleculesb)

PLAN

volume is given, so:

2 To determine the number of moles:

number of moles = 1:2 10 6kg 1 mol

28:97 g

1000 g

1 kgnumber of moles = 4.14 10 5mol

3 Using Avogadro’s number

4:14 10 5mol 6 10

23moleculesmol

number of molecules = 2:5 1019molecules

REVIEWThere are more moles in one cm3of water than one cm3 of dry air This makes sense,because the molecules in a liquid are held together by weak inter-molecular bonding,and in gases they are not; see Table 1.1 in Section 1.2 (EFM11e)

1.22: PROBLEM DEFINITIONSituation:

Start with the mole form of the Ideal Gas Law, and show the steps to prove that themass form is correct

SOLUTIONThe molar form is:

pV = nRuTWhere n = number of moles of gas, and the Universal Gas Constant = Ru =8:314 J= mol K

Speci…c gas constants are given by

molar mass of a gas

= 8:314 Jmol K

X molesg

= 8:314X J

g KIndeed, we see that the units for gas constants, R, in table A.2 (EFM11e), are

RN2 = Ru

molar mass =

8:314 Jmol K

1 mol28:02 g

1000 g

1 kg

= 297kg KJ

1.24: PROBLEM DEFINITIONSituation:

Spherical tank of CO2, does p2 = 3p1?Case 1:

p = 12 atm

T = 30 CVolume is constant inside the tankCase 2:

p = ?

T = 90 CVolume for case 2 is equivalent to that in case 1PLAN

1 Volume inside the tank is constant, as is the mass

Mass is related to volume by density

2 Use the Ideal Gas Law to …nd P2

SOLUTION

1 Mass in terms of density

For both case 1 and 2, 1 = m

V = 2; because mass is contained by the tank

2 Ideal Gas Law for constant volume

We need to convert the given temperatures to Kelvin in order to relate them to thepressures We see therefore that the ratio of temperatures in K is not 1:3 Rather,

30 C = 303:15 K, and 90 C = 363:15 K:

Therefore, T2

T 1 = 363:15 K303:15 K = p2

p 1 = 1:2) No, p2 does not equal 3p1:Instead, p2 = 1:2 p1REVIEW

When working with the IGL, you must alwasy use units for abolute temperature,

Calculate density of air using local conditions.

Compare calculated density with the value from Table A.2, and make a dation

= 1:22 kg/m3 (table value)

The density di¤erence (local conditions versus table value) is about 12% Most

of this di¤erence is due to the e¤ect of elevation on atmospheric pressure

Recommendation–use the local value of density because the e¤ects of elevation are signi…cant

REVIEW

1.26: PROBLEM DEFINITIONSituation:

1 First, apply the ideal gas law to …nd density

2 Then, calculate speci…c weight using = g:

CO 2 = 1.66 kg/m3

2 Speci…c weight

= gThus

= 1:66 kg= m3 9:81 m= s2

CO 2 = 16.3 N/m3

REVIEWAlways use absolute pressure when working with the ideal gas law

1.28: PROBLEM DEFINITIONSituation:

10 moles of methane gas; molecular weight of methan is 16g/mole

p = 5 barabsolute; 5 bar = 5 14:50psibar = 72:52inlbf2 abs; 72:52lbfin2 abs = 10; 440lbfft2

abs

T = 80 F = 539:7 RFind:

Diameter of sphere (ft)Properties:

Rmethane = 3098slugft lbfRPLAN

1 Find volume to get diameter; relate Vsphereto V term in the IGL

2 Moles of methane can be related to mass by molecular weight

3 Find V using form of Ideal Gas Law containing the mass term

4 Solve for D as per step 1

SOLUTION1

2 Methane, CH4, has a molecular weight of 16 gmol.Thus, 10 moles of methane weighs 160 g, or 0.160 kg = 0:011 slug:

3 Ideal Gas Law

p

V = 0:011 slug 3098

ft lbf slug R 539:7 R10; 440lbfft2

V = 1:756 ft34.Solve for V as per step 1

D = 3

r6V

D = 1.50 ftREVIEW

Always convert Temperature to Rankine (traditional) or Kelvin (SI) when working

Natural gas is stored in a spherical tank.

1 Mass in terms of density

1.30: PROBLEM DEFINITIONSituation:

Wind and water

T = 100 C; p = 4 atm = 405; 200 Pa

Find:

Ratio of density of water to density of air

Properties:

Air, Table A.2 (EFM11e): Rair= 287 J/kg K

Water (100oC), Table A.5: water = 958 kg/m3:PLAN

Apply the ideal gas law to air

SOLUTIONIdeal gas law

water = 958 kg/m3Ratio

water air

= 958 kg= m

3

3:785 kg= m3 water air

= 253

REVIEWAlways use absolute pressures when working with the ideal gas law

Weight (tank plus oxygen).

Properties:

From Table A.2 (EFM11e), RO 2 = 1555 ft lbf/(slug oR) :PLAN

1 Apply the ideal gas law to …nd density of oxygen

2 Find the weight of the oxygen using speci…c weight ( ) and add to Wtank.SOLUTION

1 Ideal gas law

1.32: PROBLEM DEFINITIONSituation:

Oxygen is released from a tank through a valve

V = 12 m3:Find:

Mass of oxygen that has been released

Properties:

RO 2 = 260kg KJ

p1 = 850 kPa = 850; 000 Pa abs; T1 = 17 C = 290 K

p2 = 650 kPa = 650; 000 Pa abs; T2 = 17 C = 290 KPLAN

1 Use ideal gas law, expressed in terms of density and the gas-speci…c (not universal)gas constant

2 Find the density for the case before the gas is released; and then mass fromdensity, given the tank volume

3 Find the density for the case after the gas is released, and the corresponding mass

4 Calculate the mass di¤erence, which is the mass released

SOLUTION

1 Ideal gas law

= pRT

2 Density and mass for case 1

1.33: PROBLEM DEFINITIONSituation:

Consider a mass of air in the atmosphere

V = 1:5 mi3.Find:

Mass of air using units of slugs and kg

M = V

M = 0:00237slugft3 (1:5 5280)3ft3

M = 5:23 108 slugsUnits of kg

M = 5:23 108slug 14:59 kg

slug

M = 7:63 109 kg

REVIEWNote the assumption made above stating "The density of air is the value at sealevel for standard conditions" This assumption is not safe if extreme accuracy isrequired because the mass will be somewhat less than we calculated because densitydecreases with altitude However our calculation is a good estimate for the purpose

of illustrating that we are walking around at the bottom of a heavy ocean of air!

1.35: PROBLEM DEFINITIONSituation:

Design of a CO2 cartridge to in‡ate a rubber raft

In‡ation pressure = 3 psi above patm = 17.7 psia = 122 kPa abs

Find:

Estimate the volume of the raft

Calculate the mass of CO2 (in grams) to in‡ate the raft

CO2; Table A.2 (EFM11e), R = 189 J/kg K

PLANSince mass is related to volume by m = V, the steps are:

1 Find volume using the formula for a cylinder

2 Find density using the ideal gas law (IGL)

= pRT

1.36: PROBLEM DEFINITIONFind: List three common units for each variable:

a Volume ‡ow rate (Q), mass ‡ow rate ( _m), and pressure (p)

b Force, energy, power

c Viscosity, surface tension

PLANUse Table F.1 (EFM11e) to …nd common unitsSOLUTION

a Volume ‡ow rate, mass ‡ow rate, and pressure

Volume ‡ow rate, m3= s; ft3= s or cfs, cfm or ft3= m:

Mass ‡ow rate, kg/s, lbm/s, slug/s

Pressure, Pa, bar, psi or lbf= in2:

b Force, energy, power

No solution provided, students are asked to describe the actions for each step of thegrid method in their own words.

Note to instructor - you may want to review these to …nd any excellent perspectivesraised by one or more students, to share with the class